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GM5-7: Construct and describe simple loci.

Elaboration on this Achievement Objective: 

This means that students will draw the graph of linear and simple quadratic equations. They will also be able to identify the linear equation for the graph of a given simple loci.

parabola and straight line.

 
They will also describe the common properties of points on a circle or ellipse and recognise the circle as a special case of the ellipse.

 

 

circle. 

All points on a circle are the same distance from the centre. That distance is the radius.     

 

ellipse.     

All points on an ellipse share a common sum of distances to two foci. As the foci close the ellipse “morphs” into a circle.

 

Teaching resources for this Achievement Objective:

Conic Cuts

  • Figure It Out activities
  • Geometry and Measurement
  • Level Five

This is a level 5 geometry strand activity from the Figure It Out series.

Sailing with Maths

  • Figure It Out activities
  • Number and Algebra
  • Level Five

This is a level 5 number, measurement, and geometry activity from the Figure It Out theme series.

The Running track

  • Rich learning activities
  • Geometry and Measurement
  • Level Five

The purpose of this multi-level task is to engage students in an investigation that requires them to define the dimensions of the parameters necessary to construct a described locus.

Ruler and Compass Constructions

  • Units of Work
  • Geometry and Measurement
  • Level Five

In this unit we use rulers and compasses to construct perpendicular lines and to bisect angles. These constructions are used to make a variety of polygons, nets and to illustrate loci.

Synchronised Swim Shapes

  • Units of Work
  • Geometry and Measurement
  • Level Five

The purpose of this unit is to engage the student in applying their knowledge and skills of geometric thinking to design and describe formations mathematically and the translations and/or rotations needed to create those formations.